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© Koninklijke Brill NV, Leiden, 2012 DOI: 10.1163/156658412X649986

Journal of Greek Linguistics 12 (2012) 51–83 brill.nl/jgl

A Semantics for the Particle 3ν in andoutside Conditionals in Classical Greek

Jana E. Beck,a Sophia A. Malamud,b and Iryna Osadchac*a) University of Pennsylvania

[email protected]) Brandeis University

[email protected]) University of Toronto

[email protected]

AbstractIn this paper, we provide a unifĳied semantics for the Classical Greek particle ἄν in its uses bothin and outside of conditional sentences. Specifĳically, working within the framework provided byformal semantic treatments of conditionals in Stalnaker (1968); Lewis (1973); Kratzer (1981) andsubsequent work, we propose that ἄν is a universal quantifĳier over situations—parts of possibleworlds. We also detail the interactions between ἄν and the tense and mood features in a clause,arguing, for example, that the semantics of ἄν in combination with a ‘fake’ past tense morphol-ogy (Iatridou 2000), which reflects the presence of an exclusion feature in C, gives rise to a coun-terfactual implicature. Additionally, we address the issue of the surface distribution of ἄν in theantecedents of some types of conditionals and the consequents of others and argue that, despiteits surface distribution, ἄν is always merged into the consequent of a conditional but sometimesundergoes displacement such that it appears to be located within the antecedent. Our proposalnot only illuminates a complex phenomenon in Classical Greek, but also contributes to the under-standing of the morpho-semantics of mood, conditionals, and counterfactuality in natural lan-guage.

Keywordsmodality; conditionals; counterfactuals; fake past tense; Classical Greek; cross-world situations

*) The authors would like to thank the following groups and individuals for helpful commentsand input on earlier versions of this paper: all the participants in the Fall 2010 ResearchWorkshopin the Linguistics Department at Penn, the Graduate Student Speaker Forum at Penn, the partici-pants andorganizers of the conference onAncientGreekandSemanticTheory, AnaArregui, Bron-wyn Bjorkman, Cleo Condoravdi, Dave Embick, Meredith C. Hoppin, Sabine Iatridou, MichelaIppolito, Tony Kroch, Caitlin Light, Leonard C. Muellner, and Florian Schwarz, as well as twoanonymous referees. All errors remain ours.

52 J.E. Beck et al. / Journal of Greek Linguistics 12 (2012) 51–83

We consider the uses of the particle ἄν in Classical Greek1 and propose aformal semantic analysis for them. Our goal is to provide a semantics for theparticle, accounting for the environments in which ἄν does or does not occuraswell as thepositionof this particlewithin a clause.Our analysis builds on thatof Gerö (2000) and argues that ἄν marks the presence of a universal quantifĳierover actual or possible situations.Studying the semantics of a dead language has its drawbacks—the main

one being that, in the absence of native speakers, the researcher cannot obtaintruth-value judgments directly and must rely on inferences from corpus data.However, with plentiful andwell-described corpus data, as in the case of Classi-cal Greek, this difffĳiculty can be overcome. In turn, consideration of a languagewith a rich systemof fĳine-grained distinctions in tenses, aspects, andmoods canofffer new insight into modality, quantifĳication, time, and counterfactuality—and into the connections between these phenomena cross-linguistically. Inproviding a formal treatment of ἄν, we place this particle and Classical Greekconditionals in a broader cross-linguistic typology of such phenomena.The structure of the paper is as follows. In the next section, we provide an

overview of Classical Greek verbal morphology in the relevant constructions,including conditionals, with and without ἄν. Section 2 presents the theoreticalassumptions and places our proposal within the context of the formal seman-tics literature onmodality and conditionals.Our proposal for the semantics andsyntax of the particle ἄν is presented and discussed in section 3. We concludein section 4.

. Verbal Morphology and 3ν in Classical Greek

1.1. Uses of ἄν

In the Classical Studies literature, ἄν is considered to be a part of the systemof moods (Goodwin 1890, Schwyzer 1939, Smyth 1956, Slavjatinskaja 1996, interalia). However, it is clearly separable from the verbal mood morphology. Thecomplex patterns of the co-occurrence of the particle with the various moodsand tenses in Classical Greek are described in the literature as follows:

– ἄν is never used with the imperative.– ἄν is never used with the present or present perfect indicative.– ἄν is never used with the future indicative (but see footnote 16 on page 27).

1) We restrict ourselves to the consideration of Attic and Ionic Greek of the 4th and 5th centuriesbce, excluding earlier Homeric Greek as well as the later Koine of the Greek New Testament.

J.E. Beck et al. / Journal of Greek Linguistics 12 (2012) 51–83 53

– ἄν is used with the aorist, imperfect, and pluperfect indicative.– ἄν is used with the subjunctive and optative.

The particle ἄν, when not combined with other elements into a complex form,has two kinds of uses in Classical Greek: modal and iterative. In Classical Greekconditionals, the particle ἄν has a surface distribution such that it appears inthe antecedent of some conditionals and in the consequent of others. We willbe arguing below in section 3.1 that this surface distribution of ἄν is illusory: ἄν isalways merged into the consequent of a conditional but sometimes undergoesdisplacement such that it appears to be located within the antecedent.In its iterative use in Classical Greek, ἄν occurs with past tense verbs in the

imperfect and aorist indicative (‘iterative’ uses; in these cases ἄν is optional)(Schwyzer 1939, p. 350, δ), as well as with the subjunctive in subordinate clauses(‘generic’ uses) (LSJ). Setting aside the subjunctive cases, which we address inthe next sections, the iterative ἄν construction expresses quantifĳication over(actual) past situations, as illustrated in (1). In contrast to the modal use of theparticle, there is no sense of unreality or counterfactuality here (compare 2).(1) διηρώτων ἂν αὐτοὺς τί λέγοιεν

ask.1sg.impf an them what say.3pl.prs.opt‘I used to ask themwhat (the poems) meant …’ (Plat. Apol. 22b)2

Sentences with modal ἄν involve quantifĳication over possibilities (Gerö 2000),as illustrated in comparisons between examples with and without the particle,from a grammar (2a,b) and from original texts (2c,d). On this use, sentenceswith ἄν often concern situations that are counterfactual (sometimes termed the‘irrealis’ use of the particle), as in (2d), or else possible but unlikely (sometimestermed the ‘potential’ use of the particle).

Modal use of ἄν

(2) a. ἦλθε b. ἦλθε ἄνgo.3sg.aor.ind go.3sg.aor.ind an‘He/she/it went.’ ‘He/she/it would have gone.’ (from Goodwin 1890, p. 81)

c. ταῦτα μὲν ἦν ἔτι δημοκρατουμένης τῆς πόλεωςthat prt be.3sg.impf still have_a_democracy.prs.ptcp.mp.sg the city‘That was when the city was still ruled by democracy.’ (Plat. Apol. 32c)

d. ἦν δ’ ἂν οὗτος ἢ … τῶν ἱππικῶν τις ἢ …be.3sg.impf prt an this either … the equestrian.gen.pl someone or …‘He would be a horse-trainer or … [a husbandman] …’ (Plat. Apol. 20b)

2) We depart from the Leipzig Glossing Rules’ standard abbreviations in only the following cases:impf = pst.ipfv.ind, aor = pst.pfv, mp = mediopassive, and mid = middle. All citations to Greekexamples use the standard abbreviations of the Perseus Digital Library.


In fact, the example in (2d) is in the consequent of a counterfactual condi-tional—a frequent context for themodal ἄν. The counterfactual interpretationcorrelates with the presence of this particle, and also with the past tense of theindicative mood morphology on the corresponding verb.Looking at mostly Homeric data, Gerö (2000) argues that ἄν should be given

a unifĳied analysis, contra others (e.g., Basset 1988; Monro 1891). She claims thatthe particle appears only in intensional contexts (i.e., in the scope of someintensional operator) andproposes that it canperhaps be identifĳied as an inten-sion operator that maps extensions to intensions (Montague’s ^ operator). Wewill not identify ἄν with Montague’s operator, although we agree that it marksthe presence of a specifĳic intensional operator. While iterative uses of ἄν, as in(1), appear to contradict this claim, we will argue that the particle is intensionaleven in these contexts.Dunkel (1990), p. 129 gives the following etymologies and functions for three

diffferent particles that all coalesce into the Classical Greek ἄν:3

(3) Table . Dunkel’s theory of the particles κε, κε(ν), and ἄν.

IE: 3 forms Homer: 3 forms, Dialects of the 1st Millennium (bce):3 functions all w/2 functions 1 form, 3 functions

*ke deictic potential (w/optative, main clause)*kem emphatic limiting irrealis generic (w/subjunctive, subord. clause)*an irrealis irrealis (w/indicative, main clause)

We focus on Classical Greek in this paper, but the proto-Greek and PIE ori-gins of ἄν are important because the meaning of the particle as a marker ofgeneric (iterative) universal modal quantifĳication may be the result of the factthat two functions—an irrealis4 and a generic function—were collapsed intoone particle, triggering a reanalysis of the particle’s meaning into somethingthat is roughly the combination of the two meanings. The diffferent ‘uses’ of ἄνresult from the interaction of this basic meaning with the modal and temporaloperators in its environment. In order to understand the behavior of ἄν,we nextturn to the moods and tenses in Classical Greek, and to conditionals with andwithout this particle.

3) See also Ruijgh (1996) for an alternative etymology for ἄν from κε/κεν, which, he contends,initially meant ‘then’ (> Proto-Greek *κε ‘there’). He argues that both modal and iterative rolesof κε/ἄν developed from this meaning.4) In the Classical Studies literature, the term ‘irrealis’ refers to the occurrences of ἅν in counter-factuals and, more generally, in modal contexts that may not describe reality. We will not adoptthis label, using it only when summarising Classical Studies literature.


1.2. Moods and Tenses in Classical Greek

The indicative, subjunctive, and optative moods can co-occur with the particleἄν in declarative sentences. The particle also occurs in interrogatives, but neverin imperatives; we omit non-declaratives from our discussion altogether.Indicative main verbs without ἄν are run-of-the-mill declarative statements

of fact. With ἄν, the past tenses of the indicative can be used in two diffferentconstructions. First, the ‘potential indicative’ construction uses ἄν to indicatea counterfactual possibility (Goodwin 1890; Schwyzer 1939; Smyth 1956; Slav-jatinskaja 1996, inter alia) (2b,d). On this use, the past tense is not a referenceto a past event—this is an instance of ‘fake past’ morphology (Iatridou 2000),attested in counterfactual constructions in a variety of languages. Second, the‘iterative ἄν’ constructionuses theparticle as ahabitual/genericmarker, to indi-cate a repeated event in the past (1).5Subordinate clauses with indicative verbs are described in grammars as

being ‘associated with statements of fact that refer to a defĳinite time or particu-lar occasion’ (Hoppin 2009). There are exceptions in which subordinate indica-tive verbs occur in modal contexts, most relevantly in the antecedents of Par-ticular and Counterfactual conditionals. We consider these in the next section.Main verb uses of the subjunctive are limited; they include hortatory utter-

ances (with a 1st-personplural subject, ‘let’s VP!’) and prohibitions (using aorist,negative commands only, 2nd or 3rd person singular or plural, ‘don’t VP!’/‘let Xnot VP!’). In all of its independent (main verb) uses, the subjunctive has amodaland future-oriented meaning and the resulting sentence is non-declarative.Subjunctive main verbs do not co-occur with ἄν.

5) Suggestively, Hindi also has amorpheme that is used as a habitual (iterative) and a counterfac-tual (CF) marker. Unlike ἄν, the Hindi morpheme can be repeated in some contexts to create aninterpretation that is both habitual and counterfactual (i–iii, from Bhatt 1997).

i. agar Ram phal khaa-taaif Ram fruit ate-hab‘If Ram ate the fruit (CF), …’

ii. Ram phal khaa-taaRam fruit ate-hab‘Ram eats/used to eat fruit.’ (Habitual)

iii. agar Ram phal khaa-taa ho-taaif Ram fruit ate-hab be-hab‘If Ram had been eating fruit habitually, …’ (Habitual CF)

Note also that, unlike Classical Greek ἄν, the Hindi CF marker occurs in the antecedent of acounterfactual conditional, rather than in the main (consequent) clause.


Setting aside conditionals for the moment, optative main verbs give rise totwo diffferent semantic interpretations, depending on the presence or absenceof ἄν. Without the particle, optative main verbs indicate wishes and the result-ing sentence is non-declarative; these optatives are sometimes preceded by theovert markers εἴθε or εἰ γάρ6 (4) (cf. Grosz 2011).With ἄν, this mood is termed the ‘potential optative,’ and its semantics indi-

cates the presence of a diffferent modal, indicating a future possibility or occa-sionally a present (counterfactual) possibility (Smyth 1956; Wakker 1986) (5).(4) ὦ παῖ, γένοιο πατρὸς εὐτυχέστερος

ah child become.2sg.aor.opt.mid father.gen more_fortunate‘Ah, child, may you be more fortunate than your father!’ (Soph. Aj. 550)

(5) γνοίης δ’ ἂν ὅτι τοῦθ´ οὕτως ἔχειperceive.2sg.aor.opt prt an that this so have.3sg.prs.ind‘You may see that this is so.’ (Xen. Cyrop. 1.6.21)

In subordinate temporal clauses involving quantifĳication over situations (pos-sible or actual), and in antecedents of general conditionals, the subjunctive isaccompanied by ἄν. The subjunctive in combination with ἄν distinguishes gen-eral conditionals, which canbe thought of as involving a condition that holds ofmultiple (iterated) occasions, from simple or particular conditionals, in whicha condition describes a single situation.These ‘native’ uses (i.e., described in grammars as not related to agreement

phenomena) of the moods are summarized in (6) below.

(6) The ‘native’ uses of moods in Classical Greek7

– Optative main clauses, no ἄν wishes (optative of wish)main clauses, with ἄν (unlikely) possibilities (potential optative)

– Subjunctive main clauses, no ἄν exhortation/prohibition}future-oriented

subordinate, no ἄν purpose/fear modalsubordinate, with ἄν generic/iterative

6) Literally equivalent to ‘if only’; these are not acting as modal operators, but rather indicatingthe presence of such operators elsewhere in the structure, although a formal characterization oftheir use is beyond the scope of this paper.7) Scholarsdifffer in theirdesignations for the level of likelihoodassociatedwith theuseof optativevs. subjunctive with ἄν: while some say that propositions expressed by the optative are merelypossible while ones with the subjunctive are possible and likely (Rijksbaron 1994, p. 69, Wakker1994, p. 112, Wakker 1986), others observe that the optative is used to cover both (merely) possibleas well as impossible cases, while the subjunctive is used to cover mainly the possible cases(Smyth 1956, §2322). We will follow the latter convention; whatever the designation, the use ofsubjunctivewith ἄν correlates with higher likelihood for the associated propositions than the useof the optative with ἄν.


– Indicative no ἄν specifĳic fact/situationwith ἄν irrealis/counterfactual (potential indicative)with ἄν (past) iteration (iterative indicative)

In subordinate clauses, the form of the verb can be influenced by the tenseof the main (indicative) verb: there is an alternation between the subjunctiveor indicative and the optative, termed ‘the sequence of moods’. A main verbin a non-past tense (termed ‘primary’—these are present, future, and presentperfect) has a subjunctive or indicative in the subordinate clause. In particular,indirect discourse has the indicative; purpose and fear clauses usually havethe subjunctive unless the fear concerns actual rather than possible situations,expressed using the indicative (Smyth 1956, §§2614, 2196).In a sequence of moods, a main verb in a past tense (termed ‘secondary’ or

‘historical’—these include imperfect and aorist forms, aswell as the pluperfect)optionally triggers optativemood in the subordinate clause. An indicative withἄν is never replaced by an optative—that is, a sequence-of-moods optative onlyreplaces ἄν-less indicatives (Schwyzer 1939, p. 331, γ, Smyth 1956, §2615).In contrast, when this ‘agreement-with-higher-past’ optative corresponds to

an ‘agreement-with-present’ subjunctive, any ἄν that might have been associ-ated with the subjunctive almost always drops out (Smyth 1956, §2607,Schwyzer 1939, p. 331, γ.1). That is, these ἄν-less optatives correspond to sub-junctives both with and without ἄν.Thus, subordinate clauses associated with past-tense main verbs in which

the presence of generic/iterative ἄν would be otherwise warranted, may notactually include the particle, ‘hiding’ it in the sequence-of-moods optative.Classical Greek has the sequence-of-tense phenomenon aswell, where a sub-

ordinate verb is marked by (past) tense morphology that is not interpreted butrather serves as agreement with the same tense on the main verb: “especiallyafter verbs of knowing, perceiving, showing, and verbs of emotion (rarely afterverbs of saying)” (Smyth 1956, §2624) (7).(7) ἐν πολλῇ δὴ ἀπορίᾳ ἦσαν οἱ ῞Ελληνες, ἐννοούμενοι μὲν ὅτι

in much prt perplexity be.3pl.impf the Greeks reflect.prs.ptcp.mp.pl prt that

ἐπὶ ταῖς βασιλέως θύραις ἦσανat the king’s gates be.3pl.impf

‘The Greeks were accordingly in great perplexity on reflecting that theywere at the king’sgates.’ (Xen. Anab. 3.1.2)

In addition, Greek has mood assimilation, where the verb in a subordinateclause is marked by optative, subjunctive, or indicative mood morphology tomatch the mood of the main clause. This is sometimes invoked as an expla-nation of indicative and optative mood in the antecedents of various types ofconditionals (Smyth 1956, §2183), to which we turn next.


1.3. Conditionals in Classical Greek

The use of the diffferent moods and tenses in main and subordinate clauses(with and without ἄν) sets up the pattern of conditional sentences as in (8,9). The standard labels for various types of conditionals in the grammars ofClassical Greek are taken to refer to both the meaning and the form of theseconstructions. Yet, the form is primary: for instance, Smyth (1956), §2329 givesthe moods and position of ἄν for the future less vivid conditional (8, 9h), andthen proceeds to describe several slightly diffferent uses of this construction.

(8) Table . Main “textbook” types of conditional sentences in Classical Greek.

Classics term Antecedent Consequent Meaning8

Particular (including Indic. Indic. (9a)Future most vivid, FMostV) (incl. future) (incl. future) (9b)

General (including Present Subj. + ἄν Indic. (present (9c)& Future more vivid, FMV ) & future) (9d)

Past general Opt. Indic. impf. (9e)

Present counterfactual Indic. impf. Indic. impf. + ἄν (9f)

Past counterfactual Indic. aor. Indic. aor. + ἄν (9g)

Future less vivid (FLV) Opt. (or ind.) Opt. + ἄν (9h)

The conditionals in the table are grouped according to theirmoods and the useof ἄν.Particular conditionals use the indicative mood without ἄν in both the ante-

cedent and the consequent (9a). When both the antecedent and the conse-quent of a particular conditional have future verbs, the construction is labeledFuture Most Vivid (FMostV, 9b).Non-past general conditionals use subjunctive with ἄν in the antecedent

(the generic ἄν), and indicative mood in the consequent. When the indicativemain verb is in the present, the label is Present General (9e), while generalconditionals with future verbs in the consequent are termed FutureMore Vivid(FMV, 9d).Past general conditionals have optative verbs in the antecedent and indica-

tive imperfect in the consequent (9e). They do not include ἄν; however, sincethemain verb is in the past tense, the sequence-of-moods optative in the ante-cedent may be “hiding” the particle.

8) This is just a preliminary and pre-theoretical indication of the semantics of these sentences. Athorough discussion, based on the literature and our corpus study, follows.


Next, constructions labeled Counterfactual use indicative in the antecedent,and indicative with ἄν in the consequent. Counterfactuals using imperfect inboth clauses are termed Present Counterfactual (9f), while those using aoristverbs are Past Counterfactual (9g).Finally, conditionals which use optative verbs in both antecedent and con-

sequent, with ἄν in the consequent, are called Future Less Vivid (FLV, 9h).We exemplify these constructions below, with a brief indication of their

semantics.

Particular: A single-case conditional regarding a specifĳic situation in the actual world

(9) a. εἴπερ γε Δαρείου καὶ Παρυσάτιδός ἐστι παἶς … οὐκif indeed Darius and Parysatis be.3sg.prs.ind son not

ἀμαχεὶ ταῦτ´ ἐγὼ λήψομαιwithout_resistance these I take.1sg.fut.ind

‘If indeed he is the son of Darius and Parysatis, I will not take these things withoutresistance.’ (Xen. Anab. 1.7.9)

Future Most Vivid: A conditional regarding a specifĳic situation in the future

b. ἀποκτενεῖς γάρ, εἴ με γῆς ἔξω βαλεῖςkill.2sg.fut.ind for if me land.gen.sg out throw.2sg.fut.ind‘For you will slay me if you cast me out of the land.’ (Eur. Phoen. 1621)

General present: Generalization in the present

c. καὶ ἐ-ὰν ἴσοις ἴσα προστεθῇ, τὰ ὅλα ἐστὶν ἴσα.and if-an equals equals add.3sg.sbjv.pass, the wholes be.3sg.prs.ind equal‘And if equals are added to equals, the wholes are equal.’ (Euc. 1.CN.2)

Future More Vivid: Generalization in the future

d. τί ἔσται τοῖς στρατιώταις, ἐ-ὰν αὐτῷ ταῦταwhat be.3sg.fut.ind.mid the soldiers.dat if-an him this

χαρίσωταιoblige.3pl.aor.sbjv.mid

‘What will the soldiers have, if they oblige him in this?’ (Xen. Anab. 2.1.10)

General past: Generalization in the past

e. εἴ πού τι ὁρῴη βρωτόν, διεδίδουif anywhere any sees.3sg.prs.opt food give_out.3sg.impf‘If he saw any food anywhere, he gave (it) out.’ (Xen. Anab. 4.5.8)


Present counterfactual: Counterfactual regarding the present

f. ταῦτα δὲ οὐκ ἂν ἐδύναντο ποιεῖν, εἰ μὴ καὶ διαίτῃ μετρίᾳthese but not an can.3pl.impf do.ipfv.inf if not also diet measured

ἐχρῶντο.use.3pl.impf

‘But they would not be able to do these things, if they were not also following atemperate diet.’ (Xen. Cyrop. 1.2.16)

Past counterfactual: Counterfactual regarding the past

g. οὐκ ἂν ἐποίησε ᾽Αγασίας ταῦτα, εἰ μὴ ἐγὼ αὐτὸν ἐκέλευσα.not an do.3sg.aor.ind Agasias these if not I him order.1sg.aor.ind‘Agasias would not have done these things, if I had not ordered him (to).’

(Xen. Anab. 6.6.15)

Future less vivid: Statement about unlikely or possible situation in the future

h. … θαυμάζοιμ´ ἂν εἰ οἷός τ´ εἴην ἐγὼ ὑμῶν ταύτηνbe_surprised.1sg.prs.opt.mp an if able prt be.1sg.prs.opt I you this

τὴν διαβολὴν ἐξελέσθαι ἐν οὕτως ὀλίγῳ χρόνῳ …the prejudice take_away.pfv.inf.mp in so little time

‘… I would be surprised if I were able to remove this prejudice from you in so short atime …’ (Plat. Apol. 24a)

Several generalizations emerge from the table and examples in (9).First,we see that the alternationbetween subjunctive + ἄν andoptative in the

antecedents of general conditionals is an instance of the sequence-of-moodsphenomenon. This is suggested both by the correlation with the tenses of theindicative in the main (consequent) clause, and also by the presence of quan-tifĳication over situations in the meaning of these conditionals. That is, whileall conditionals are analyzed in formal semantics as involving quantifĳicationover worlds or situations, particular conditionals nevertheless can be thoughtof as referring to a specifĳic topic situation in the actual world (and its epis-temic counterparts)—asingle-case conditional (Kadmon 1987). In contrast, thepresent, future, or imperfect indicative verbs in the consequent clauses of gen-eral conditionals do not refer to a specifĳic topic situation, but rather to a set ofsituations over which the generalization holds—multi-case conditionals (Kad-mon 1987).Second, note that the only way to achieve a counterfactual interpretation

is by using the particle ἄν, which in the “textbook” conditionals is located inthe main clause. If we take seriously the implicature of low likelihood of theantecedent situation inFLVconditionals, thenwecan includeFLVconditionalsin this counterfactual group, and say that in these “textbook” cases, ἄν occurs


in the main clause if and only if such a contrary-to-fact inference is present.9In any case, the optative + ἄν in the FLV and the past indicative + ἄν in thecounterfactual conditionals are simply instances of the potential optative andpotential indicative constructions. The counterfactual and FLV conditionalscan be either single- or multi-case, but tend to be mostly the former.Thesemain-clause constructions with ἄν, together with the describedmood-

assimilation in Classical Greek subordinate clauses, suggests that we shouldtreat consequent-clause morphology in conditionals as more semanticallymeaningful than antecedent morphology in the counterfactual and FLV condi-tionals. We seek to explain the various interpretations that arise in condition-als with and without ἄν through the interaction of this particle with the mood,tense, and aspect of the main (consequent) clause, where possible.Third, the correlation between a higher past tense and a lower optativemood

in the sequence-of-mood scenarios raises the question of underlying structurein the sentences with potential optatives—could such sentences, too, have(covert) past higher in the structure? If the optative in subordinate clauses andthe potential optative are instances of the same phenomenon, why does thelatter, but rarely the former, co-occur with the particle ἄν?Finally, note that the past morphology in both the antecedent and conse-

quent of the present counterfactual conditionals does not seem to be inter-preted as referring to the past. What is the semantic contribution of this ‘fakepast,’ and what is the explanation for its presence?In the next section, we turn to this fĳinal question in the context of formal

semantics, and use it as a key to building our proposal for the semantics of ἄν.

. Previous Research: Conditionals, Counterfactuals, and Past

2.1. Conditionals and Situations in Formal Semantics

In most formal semantic treatments following Stalnaker (1968); Lewis (1973);Kratzer (1981), and subsequent work by these and other authors, conditionalsare thought of as involving quantifĳication over possibilities. Possibilities areusuallymodeled as possible worlds or related objects: possible situations (partsof possible worlds) or else tuples of entities including possible worlds (e.g.,world-assignment pairs).

9) The distinction between the location of the particle in the main vs. subordinate clause in the“textbook” conditionals seems to predict a correlation between the surface syntactic position ofἄν and the interpretation of the sentence. As we make clear in section 3.1, we claim that there isno such correlation, and propose a diffferent explanation for the diffference in the surface positionof ἄν, which has no bearing on its semantics.


Quantifĳicational structures include three main parts: a modal operator (aquantifĳier over possibilities), a restrictor narrowing the range of the quantifĳierto a contextually-determined set of possibilities, further narrowed down bythe contents of the if -clause, and fĳinally the nuclear scope of quantifĳication—the condition that holds of the quantifĳied possibilities, expressed by the main(consequent) clause (Montague 1974; Partee 1991; Kamp and Reyle 1993, interalia).Themodal quantifĳiermay be overt, as in (10), or else silent. The contextually-

determined set of possibilities restricting the quantifĳication even before theantecedent is considered is selected based on the lexical properties of themodaland the influence of context. Following Kratzer (1981); Kratzer (1991), the con-textual contribution to modal interpretations is separated into two dimen-sions—the modal base and the ordering source.

(10) a. If the lights are on, Mary must be home.b. If we are on Route 183, we might be in Lockhart. (von Fintel and Heim 2009)

First, the accessibility relation provides themodal base, a conversational back-ground against which the modal is interpreted—that is, the accessibility rela-tion is a function which, for every possible world (including the actual one),provides the set of worldsmost relevant for themodal. Thus, an epistemic con-versational background is the set of propositions representing what we know,a legal conversational background is the set of propositions representing whatthe law provides, etc. (Kratzer 1991).In addition, not every world helpfully provided by the accessibility relation

is as good as every other world. Here is where similarity comes in—we onlywant thoseworlds which are close-enough (or closest) to the actual world. Thatis, even in counterfactual worlds, we want some features of the actual worldpreserved. In sentences such as (11), the conversational background ensuresthat we only consider possibilities inwhich spiders are bornwith eight legs.Wedon’t want to consider a world in which I am a spider who, due to misfortune,lost a leg and now only has seven—yet such a world may well be a memberof the accessible set. Thus, various authors have proposed diffferent similaritymechanisms that are responsible for selecting the closest, best, and most law-like of the accessibleworlds. InKratzer’s framework, the ordering source is a setof propositions that imposes a partial ordering on themodal base, based on thenumber of these propositions which are true in a world. The ordering sourcecan be deontic (themore actual-world laws are followed in w, the closer w is tothe actual world), stereotypical (the closer w is to the normal course of events,the closer it is to the actual world), etc.

(11) If I were a spider, I would have eight legs (in view of the biological properties of spiders inthe actual world).


In our proposal for Classical Greek conditionals, we will utilize situations—parts of possible worlds. Situation semantics (Kratzer 2009) was developed fĳirstby Jon Barwise and colleagues (Barwise 1981; Barwise and Perry 1983), formaliz-ing the idea originally attributed to J.L. Austin that utterances are about partic-ular situations (Austin 1979).To take a classic example, consider the sentence ‘Claire has the three of

clubs’:

We might imagine, for example, that there are two card games going on, one across townfrom the other: Max is playing cards with Emily and Sophie, and Claire is playing cards withDana. Suppose someone watching the former game mistakes Emily for Claire, and claimsthat Claire has the three of clubs. She would be wrong on the Austinian account, even ifClaire had the three of clubs across town. (p. 122 Barwise and Etchemendy 1987)

Possibilistic situation semantics extends the idea of evaluating utterances rela-tive to situations to evaluating predicates relative to situations. All propositionsare treated as sets of possible situations,which are ordered by a ‘part of’ relation≤ such that if s ≤ s′, then s + s′ = s′. The maximal situation that any situation s isrelated to by ≤ is the possible world ws—that is,ws is not a part of any situationother than ws.Below is a good example that shows the usefulness of possibilistic situation

semantics:

(12) Everyone is asleep and is being monitored by a research assistant.

The quantifĳier ‘everyone’ ranges over people who are part of the ‘research-subject’ situation, and thus does not include research assistants.The connection to possible worlds allows situations to be used in analyzing

modal sentences, including conditionals.InKratzer’s (2009) situation semantics, situations are treated like Lewis-style

individuals: each is a part of at most one world, but can have counterparts inother worlds. Thus, Arregui (2009) offfers a semantics for English counterfactualconditionals with would which relies on the notion of a ‘modal part of’ relationbetween situations:

(13) Given two situations si and sj, si is a modal part of sjsi ≤m sj ifff there is some st such that st is a counterpart of si and st ≤ sj.

The modal part of relation between situations in diffferent worlds is a specialcase of the counterpart relation between diffferent-world individuals (Lewis1971). Would is analysed as a universal modal. Its modal base is the set of allsituations from diffferent possible worlds in which a contextually-salient set oflaws is observed. The situations are ordered based on their similarity to theactual-world situation of which the entire conditional is predicated: thus, forArregui (2009) the similarity-based counterpart relation between situations


replaces the ordering source of Kratzer (1991). In this framework, (11) receivesthe following semantics:

(14) (11) is true of the actual-world situation s, given by the past tense,ifff every law-like situation sL′ such that s ≤m sL′ and my counterpart in sL′ is a spider,extends to a lawlike situation sL′′ such that sL′ ≤ sL′′ and my counterpart has eight legs in

sL′′,where sL is a situation that satisfĳies the set of actual-world laws L salient in the context

(including biological properties of spiders).

This notion of similarity focuses only on the relevant features of the actualworld. For example, in (11), only the features of the actual-world that relateto spiders matter in determining similarity, while irrelevant features such asgeopolitical history are ignored in selecting the best possibilities to quantifyover. Note that the entire conditional describes a property of the actual-worldsituation s: this kind of predication in which amodal property is ascribed to anactual-world individual (and its counterparts) is termed de re modal predica-tion. Thus, (11) has de re predication of s and of me.In our analysis of the particle ἄν and of Greek conditionals we will adopt

many features of Arregui’s framework, including a modal base that consists ofsituations, an ordering that depends on a similarity-based counterpart relation,and de re modal predication.

2.2. Fake Past in Conditionals—Iatridou (2000)

In a seminal paper, Sabine Iatridou considers the interpretation of past-tensemorphology (among other elements) in conditionals. English present counter-factual conditionals of the form (15a-i) convey the information that the ante-cedent clause and the consequent clause don’t hold at present (15b-i). Pastcounterfactuals of the form (15a-ii) convey that the antecedent and consequentdo not hold in the past (15b-ii).

(15) a. i. If he were smart, he would be rich.ii. If he had been smart, he would have been rich.

b. i. He is not smart now; he is not rich now.ii. He was not smart, and he was not rich (past situation—no information about the

present).

The information in (15b) is not asserted: thus, for instance, we can follow up on(15a-i) with the assertion that the antecedent holds, without a contradiction; orwith the assertion that the antecedent is false, without a redundancy.

(16) a. In fact, he’s stinking rich, so I guess he’s smart, too.b. In fact, he’s dirt poor, so I guess he’s stupid.

Thus, Iatridou (2000) concludes that counterfactuality arises as an implicature.


We tentatively suggest that, in Classical Greek, counterfactuality in sen-tences with ἄν is an implicature as well.10The conditionals in (15a, 17) all have fake past tense in them, which must

appear in the antecedent and consequent in both English and Modern Greek:in (15a-i) he is not rich/smart now; likewise in (15a-ii) he is not rich/smart atsome point in the past (so, it’s past not pluperfect).Iatridou argues that past conditionals (15a-ii) do have one layer of non-fake

past, since they cannot be realizable in the future, in contrast to English FutureLess Vivid (FLV) conditionals, such as (17b):

(17) a. If he had taken the syrup, he would’ve gotten better. (Not good as an instruction to acaregiver.)

b. If he took the syrup, he would get better. (OK as an instruction to a caregiver.)

The FLV conditional (17b), (15a-ii) conveys the implicature that in the actualworld (w0) the negation of the antecedent (he does not take the syrup) is morelikely to become true than the antecedent (he takes the syrup);11 in suitablecontexts it can also be used to emphasize speaker ignorance about whether por not p will become true.Iatridou (2000) proposes that the past tense morpheme is actually an ‘exclu-

sion’ morpheme (18). Iatridou assumes, after Kamp and Reyle (1993), amongothers, that future is really a modality, and therefore the only true tenses arepast and present.12 Thus, when interpreted temporally, the exclusion mor-pheme indicates that the topic time precedes the utterance time (18b). Wheninterpretedmodally, it indicates that the topicworlds do not include the actualworld (18c). Thus, without forcing counterfactuality, on its fake-past (modal)use, the morpheme leads to an implicature that the proposition is not appliedto the actual world because it is false in the actual world—the counterfactualimplicature.

(18) a. [[+excl]] = The topic time or world excludes the utterance time or worldb. Applied to times—exclusion from utterance time (now)→ true pastc. Applied to worlds—the topic worlds don’t include the actual world→ fake past,

counterfactual implicature

What is the relationship between the semantics of English FLV (17b) and pres-ent counterfactual conditionals (15a-i)?

10) Note that here we are in disagreement with Wakker (1994), pp. 150–155, who treats at leastsome counterfactual conditionals in Ancient Greek as presupposing falsity of the antecedent.11) But see Giannakidou (2009) for a discussion of the FLV in Modern Greek and criticism ofIatridou’s analysis with regard to the likelihood that the negation of the antecedent in an FLVwill come true.12) Alternatively, exclusion can be supplemented by a precedence condition, vacuous in themodal case.


It may seem that the FLV cannot contribute a counterfactual implicaturesince future cannot be factual to begin with. However, the FLV conditionalsoften do contribute an implicature that in the actual world the negation of theantecedent is more likely to become true than the antecedent proposition. In away, this is the same counterfactuality implicature as in the present counterfac-tual, but conveyed with respect to a point in the future rather than the present.We follow Iatridou (2000) in considering this to be the same implicature in allcases, whichwe continue to term “counterfactual” even in the FLV conditionalsin Classical Greek.As with any implicature, the counterfactual implicature is absent in those

contexts where it is clear that the antecedent is true, or will become true in theactual world. After uttering the FLV conditional in (19), Socrates proceeds totestify that he has seen the antecedent fulfĳilled. We can conclude that in thiscase, the counterfactual inference is canceled.13

(19) εἰ οὖν ὑμῶν οἱ δοκοῦντες διαφέρειν … ᾑτινιοῦν ἀρετῇ τοιοῦτοιif then you those seem.prs.ptcp.pl be_superior.ipfv.inf whatever virtue such

ἔσονται, αἰσχρὸν ἂν εἴηbe.3pl.fut.ind.mid shameful an be.3sg.prs.opt

‘If then those of you who are supposed to be superior … in any virtue whatsoever are tobehave in such a way, it would be disgraceful.’ (Plat. Apol. 35a)

Iatridou (2000) argues that the exclusion feature, introduced by the past tensemorphology in FLVs and in present and past counterfactuals in English andModern Greek, is responsible for the counterfactual implicatures in these con-structions.Subsequent research indicates that modal interpretations of the exclusion

feature correspond to a higher syntactic position of thismorpheme than on thetemporal interpretation. Thus, Bjorkman (2011) argues that when this featureis interpreted in the T(ense) position, it yields past time, but it can also beinterpreted inC(omplementizer) position,where it yieldsmodalmeanings thatdo not include the actual world.

13) Wewere unable to fĳind any examples of Present or PastCounterfactual conditionalswhere theantecedentwas true; however,we did fĳindmanyexampleswhere the antecedentwas presented aspossible. This diffference in the strength of counterfactuality expressed in the FLV conditionals onthe one hand, and Counterfactual conditionals on the other hand, is probably due to the nature ofthe speaker’s evidence for statements about the future (indirect at best), in contrast to statementsabout the present and past (where speakers are presumed to be well-informed, all else beingequal).


. Proposal for 3ν

We propose that ἄν represents a modal universal quantifĳier (similar to English‘would’), ranging over situations (20).

(20) [[ἄν]]g,w = λ p〈st〉.λ q〈st〉.λ s ≤ w [(∀ s′ ∈ M : p(s′) = 1) ∃ s′′ [s′ ≤ s′′& q(s′′) = 1]]Paraphrase: The conditional is true of an actual-world situation s ifff, whenever the ante-cedent is true in a situation s′, the consequent is true in a situation s′′ which extends s′.

The situations that this quantifĳier ranges over (s′ ∈M in the formula)may comefrom one or more possible worlds (cf. Arregui 2009); this allows the particleto have modal interpretations, unlike a universal quantifĳicational adverb suchas always. The nature of the set M will largely determine the interpretation ofἄν in the specifĳic examples. The modal uses of ἄν arise when M contains onlymaximal situations (worlds), and the formula in (20) becomes a standard uni-versal modal. Iterative uses result when M contains only subsituations of theactual world. The use of ἄν in antecedents of General conditionals (the genericuse) combines the features ofmodal and iterative uses—quantifĳication in thesecases is over non-maximal subsituations of diffferent possible worlds. The fea-tures of the actual-world situation s (currently absent from the body of the for-mula) and other temporal and modal ingredients in the sentence, discussed insubsection 3.2, will participate in establishingM to derive the various uses of ἄν.Before we proceed to examine the semantic derivations involving ἄν, let us

briefly consider the syntax of the particle.

3.1. The Syntax of ἄν

Given that thenon-unifĳied analyses of ἄν generally divide theuses of ἄν into twogroups depending onwhether the particle occurs in the antecedent or the con-sequent of a conditional, solving the problem of the position of ἄν in condition-als is essential to arguing for a unifĳied analysis. In order for the semantics andthe syntax to match up well, ἄν must c-command its restrictor, the antecedentclause. The main problem in Classical Greek is that ἄν at least appears to belocated within the restrictor clause of some conditionals (namely, future morevivid and present general conditionals). In this section, we will argue that ἄν isalways merged into the consequent of a conditional but sometimes undergoesdisplacement such that it appears to be located within the antecedent.Syntactically, the consequent of a conditional is the matrix clause of a sen-

tence, and the antecedent is an adjunct CP headed by the ‘if’ element and right-adjoined at VP (Bhatt and Pancheva 2006). Under the hypothesis that ἄν islocated within the consequent of all Classical Greek conditionals, this yieldsthe schematic structure for a conditional in (21).


(21)

In general, ἄν occurs second, second to last, or last in the IP domain of thesentence, suggesting a position at the edge of the IP domain (cf. Smyth 1956,§ 1764, “ἄν does not begin a sentence or clause.”). It is linearized either on theright or left, with a process of local dislocation—an operation at PF that efffectsafffĳixation of one element to another under linear adjacency (Embick andNoyer1999; Embick and Noyer 2001; Noyer 2001; Embick 2003), inverting the positionof ἄν and the fĳirst or last word in the IP domain to satisfy ἄν’s enclitic nature.The antecedent generally moves to precede the consequent, via post-syntacticfronting. Thus, the structure of (22) at LF is as in (23).(22) εἰ μὲν πρόσθεν ἠπιστάμην, οὐδ’ ἂν συνηκολούθησά σοι.

if prt before know.1sg.impf not_even an accompany.1sg.aor.ind you‘If I’d known this before, I wouldn’t even have accompanied you.’ (Xen. Anab. 7.7.11)

(23)14

14) We use TP/VP in places in order to remain agnostic on various irrelevant syntactic issues inClassical Greek—namely, whether the verb raises to T and where sentential negation is located.


Deriving the second-in-IP position evidenced in (22) is a two-part process. First,ἄν together with the restrictor is fronted and adjoined at the TP level (24).

(24)

This is followed by further fronting of the restrictor alone (25).

(25)

Finally, both the sentential particle μέν and ἄν undergo local dislocation and asa result are displaced one word to the right (26).


(26)

Alternatively, in some conditionals (27), ἄν appears as the second-to-last or lastword in the matrix clause.(27) εἴης φορητὸς οὐκ ἄν, εἰ πράσσοις καλῶς

be.2sg.prs.opt bearable not an if do.2sg.prs.opt well‘You would be unbearable if you were doing well.’ (Aesch. PB 979)

The variability between placement last in the matrix clause and second-to-last must mean that local dislocation is optional at the right edge, as opposedto being obligatory at the left edge. In contrast to the derivation for (22), thederivation for (27) is shorter, all processes are likely prosodically motivated,operating apart from the semantics. No processes are strictly necessary.

(28)


At fĳirst glance, it may appear very difffĳicult to derive the proper word orderwhen ἄν is in the antecedent, as occurs in the present general and future morevivid conditionals (29).(29) ἐ-ὰν ζητῇς καλῶς, εὑρήσεις

if-an seek.2sg.prs.sbjv well fĳind.2sg.fut.ind‘If you seek well, you will fĳind.’ (Plat. Gorg. 503d)

The solution is to use the same LF as in (23) and (28) above (30).

(30)

Then, the process of local dislocation operates immediately, cliticizing ἄν tothe proclitic conditional complementizer (31); this is optionally followed byfronting of the now inseparable ἄν + restrictor complex (32).

(31)


(32)

Thus, a unifĳied syntactic treatment of ἄν enables us to proceed with a unifĳiedsemantics for the particle.

3.2. Semantics of Counterfactual and Iterative Uses of ἄν

In counterfactual conditionals (present and past), as well as in potential indica-tivemain-clause examples, the interpretations arise from the following ingredi-ents. First, thepast tensemorphologyon themain-clause verb represents agree-ment with the higher exclusion feature, interpreted modally. This means thatthe topic situations are not part of the actual world. Extending Iatridou (2000)’sanalysis, we propose that on its modal use, the exclusion feature gives rise to aset of maximal non-actual topic situations—that is, to a set of non-actual topicworlds.Second, with respect to quantifĳication, topic denotations are part of the

restrictor (Partee 1991), regardless of their position. Thus, even though it is notsyntactically part of the conditional antecedent, the exclusion feature partiallydefĳines a modal base: a modal quantifĳier, such as ἄν, will range over worlds(maximal situations) that do not (necessarily) include the actual world.The modal ἄν quantifĳies over this set, further restricted by certain laws and

features of the actual world, and by the antecedent of the conditional.Third, turningnow to these laws and features,we follow (Kratzer 1991) in con-

ceiving of these restrictions on modal quantifĳiers as imposed in two separatesteps. These steps operate in all conditionals, and represent a contextual con-nection between the antecedent and the consequent. As a fĳirst step, the contex-tual constraints, which we represent as a predicate of possibilities Cont, influ-ence the accessibility relation. These constraints onpossibilities include a set ofsalient actual-world laws; accessible worlds in the modal base are restricted tothose in which these laws operate (compare Kratzer 1991; von Fintel 1994; von


Fintel and Heim 2009, for discussion of restrictions on modal quantifĳiers). Forinstance, in the deontic conditional (33a), quantifĳication is over contextually-appropriate (situations that are parts of) worlds in which dormitory rules areobeyed.

(33) a. If you bring a guest to your dorm, you must meet in the lounge.b. If you brought a guest into your bedroom, the R.A. would scream at you.

In part inspired by the discussion of counterfactual conditionals in Arregui(2009), we propose that these laws can be partially reifĳied as features of actual-world situations—for instance, in (33a), the existence of a dormitory rule, per-haps posted in writing at the dorm entrance, or simply existing in the abstract.We depart from Arregui’s proposal in that these facts are not represented asactual situations. In general, as a second step constraining the modal, we pro-pose a similarity relation based on reference to specifĳic actual-world facts. Theconditional or modal sentence as a whole is predicated de re of these facts,just as Arregui (2009) proposes for situations. Thus, for instance, in (33a), weconsider a set of situations in which dorm-rules are obeyed; within this set, weselect situations in which the posted dorm-rule is in force.We avoid conceptualizing the relevant features of the actual world as a sin-

gle situation in order to maintain a uniform analysis for diffferent kinds of con-ditionals and constructions with ἄν. A res situation works for the counterfac-tual cases—the features it represents are present in the accessible situationsif those situations contain a counterpart of the res situation. In contrast, sev-eral non-overlapping situations in the actual world cannot all contain the ressituation as a part; yet we will need to quantify over just such a set of situ-ations to model iterative uses of ἄν. However, such situations can all sharea feature or fact—for instance, the same dorm rule may be operational inthem.Importantly, unlike Arregui, wemake no connection between these features

of the actual world and the past tensemorphology in counterfactual sentences:thus, in (33b), we select the presently-posted dorm-rule as the res of modalpredication.Fourth, the propositions denoted by the subordinate andmain clauses of the

conditional are tenseless—the situations in which these propositions are trueare not restricted with respect to their temporal location.The diffference between past and present counterfactuals is aspectual (see

(34) repeated from (9e–f) above). Imperfect is compatible with the eventualityoverlappingwith (non-past) reference time. In contrast, “…the aorist indicativeis most commonly used to signify that the state of afffairs concerned is com-pleted with regard to (is anterior to) a state of afffairs mentioned in the ensu-ing context … Sometimes, however, the state of afffairs expressed by the aorist


indicative is completed with regard to (is anterior to) a state of afffairs men-tioned in the preceding context (‘past-in-the-past’)” (Rijksbaron 1994,p. 20). Since future completed events in Classical Greek are marked as future,rather than aorist, this leads to an inference that the completed eventualitytook place in the past. Thus, like their English counterparts, the Classical Greekpast counterfactuals convey that the eventualities in the antecedent and con-sequent are temporally past, despite morphological diffferences with English.

Present counterfactual: Counterfactual regarding the present

(34) a. ταῦτα δὲ οὐκ ἂν ἐδύναντο ποιεῖν, εἰ μὴ καὶ διαίτῃ μετρίᾳthese but not an can.3pl.impf do.ipfv.inf if not also diet measured

ἐχρῶντο.use.3pl.impf

‘But they would not be able to do these things, if they were not also following atemperate diet.’ (Xen. Cyrop. 1.2.16)

Past counterfactual: Counterfactual regarding the past

b. οὐκ ἂν ἐποίησε ᾽Αγασίας ταῦτα, εἰ μὴ ἐγὼ αὐτὸν ἐκέλευσα.not an do.3sg.aor.ind Agasias these if not I him order.1sg.aor.ind‘Agasias would not have done these things, if I had not ordered him (to).’

(Xen. Anab. 6.6.15)

Finally, an (optional) agreementmechanism responsible formood assimilationin Classical Greek results in indicative mood in the antecedent.These ingredients combine as in (35), to create a meaning in (36b) for a

counterfactual sentence such as (36a, 2d)

(35)


(36) a. εἰ μέν σου τὼ ὑεῖ πώλω … ἐγενέσθην, … ἦν δ’if prt your the sons colts … become.3du.aor.ind.mid … be.3sg.impf prt

ἄν οὗτος … τῶν ἱππικῶν τις …an this the equestrian someone …

If your two sons had happened to be two colts, … this (one) would be a horse-trainer …’(Plat. Apol. 20a)

b. [[(36a)]]g,w = λ s ≤ w [ ( ∀s′ : contribution of ἄνyour sons are born as calves in s′ contribution of if-clause& s′ ∈ { w : w =/ w0 & Cont(w)} Ri partially provided by Excli& ∃ s′′′ [ actual-world facts g(17) are in force in s′′′ & s′′′ ≤ s′ ] ) SIM with facts 17∃ s′′ [ s′ ≤ s′′& g(9) is a horse-trainer in s′′ ] ] contribution of then-clauseParaphrase: the conditional is true in a situation s ifff in a set of situations s′

– which are maximal non-actual law-like situations (i.e., non-actual law-like worlds),(exclusion feature selects the modal base)

– in which there is a counterpart of actual-world facts referred to by g(17),(similarity with res facts provides the ordering source)

– and in which (counterparts of) your sons are born as calves,(if-clause)

– every situation s′ extends to the situation s′′, such that (counterpart of) g(9) is a horse-trainer in s′′(then-clause)

Turning to the iterative uses of ἄν, we propose that the particle has exactlythe same meaning as before (20), but involves a very diffferent accessibilityrelation—one that instead of providing diffferent possible worlds, gives a setof situations which are all part of an actual past situation invoked by the past-tense morphology in T (imperfect or aorist). The LF is otherwise identical tothe one for a counterfactual conditional, butwith an implicit antecedent clause(that is, no if-clause in the structure). The indicativemood is chosen by default.Thus, an example such as (1), repeated below, is analyzed as in (37).

(1) διηρώτων ἂν αὐτοὺς τί λέγοιενask.1sg.impf an them what say.3pl.prs.opt‘I used to ask themwhat (the poems) meant …’ (Plat. Apol. 22b)

(37) a.[[(1)]]g,w = λ s ≤ w [ ( ∀s′ : contribution of ἄν& s′ ≤ w Ri limits s′ to actual-world situationstime (s′)⊆ topic interval t & t precedes now Ri partially provided by Excli& ∃ s′′′ [ actual-world facts g(15) hold in s′′′ & s′′′ ≤ s′ ] SIM with facts 15& Cont(s′) ) ‘s′ is contextually appropriate’∃ s′′ [ s′ ≤ s′′& Socrates asks g(5) in s′′ ] ]Paraphrase: the sentence is true in a situation s ifff in a set of situations s′

– which are subsituations of the actual world,(modal base contextually limited to actual situations)


– and which precede the utterance time,(exclusion in T limits modal base to past situations)

– in which the facts referred to by g(15) hold,(similarity with res facts provides the ordering source)

– every situation s′ extends to a situation s′′ in which Socrates asks g(5)(main clause)

(37) b.

Our analysis of these two core uses of ἄν places the semantic diffferencesbetween them in the choice of the accessibility relation, which, in turn, relatesto the interpretation of past-tense morphology as true or ‘fake’ past. The pro-posal treats modal sentences as predicates of actual-world facts, which are rep-resented as features of situations. Next, we explore the consequences of thisapproach for other sentences with and without ἄν.

3.3. Conditionals with and without ἄν

Wenow turn to general conditionals, startingwith thepresent general (PG) andfuturemore vivid (FMV) conditionals. Consider the example (9c), repeated andanalyzed below.(9c) καὶ ἐ-ὰν ἴσοις ἴσα προστεθῇ, τὰ ὅλα ἐστὶν ἴσα.

and if-an equals equals add.3sg.sbjv.pass, the wholes be.3sg.prs.ind equal‘And if equals are added to equals, the wholes are equal.’ (Euc. 1.CN.2)

These sentences express a generalization over present or future situations—thus, the tense morphology on the indicative main verb is interpreted, andthere is no exclusion feature in C giving rise to a counterfactual implicature.The tensemorphology invokes situations overlappingwith (the counterpart of)now in present general conditionals, and future with respect to now in FMV


conditionals. PGs and FMVs are multi-case conditionals,15 which can be mod-eled using quantifĳication over situations, where multiple situations per worldcan be included. Thus, the accessibility relation in these cases is very similar tothe one used in the iterative-ἄν examples (37), with the only diffference beingthat it is not restricted to parts of an actual past situation.16In a sense, this use of ἄν blends elements of the iterative andmodalmeanings

associated with the particle. The accessibility relation involves situations frommultiple worlds (like counterfactuals). However, situations from the actualworld are also included, and they come from (counterparts of a) non-past timeinterval (like iterative uses) (38).In the antecedents of these conditionals, Classical Greek uses the subjunc-

tive mood, which in subordinate clauses normally reflects the presence of ahigher modal, and higher non-past morphology. Without attempting to pro-pose a semantic analysis of the subjunctive mood, we note that, as in manyother kinds of subordinate clauses, subjunctive verbs in general condition-als indicate the following confluence of material higher in the structure: (i)the presence of a quantifĳier (as opposed to non-quantifĳicational contexts), (ii)quantifĳication over situations (rather than whole worlds), and (iii) a non-past,non-exclusivemain clause (the absence of the +excl feature) (39). The particleἄν cliticizes onto the conditional complementizer, essentially becoming a partof the antecedent.

15) Note that on this point we are in agreement withWakker (1994), p. 111:

… I claim that the division particular [= our single-case] vs. general [= ourmulti-case] condi-tionalmust be used (as an auxiliary factor) todescribe theGreek conditional system: periodsconsisting of ἐάν with subjunctive and a present indicative in the main clause, and periodsconsisting of εἰ with optative and an imperfect in themain clause are invariably general. Thegeneral character is accompanied by formal marking and is not context-dependent. In allother cases, however, it is the context that decides whether the if -clause in question mustbe interpreted as specifĳic or general.

16) In fact, there are an unknown number of examples of future indicative main verbs with ἄνand no antecedent that can be seen as exactly parallel to the iterative ἄν (16). The number of theseexamples is unknown because they are usually, if not always, emended by editors (Smyth 1956,§ 1793, Gildersleeve 1900, §432).

In this example, the original future indicative προτρέψετε, attested in two manuscripts, hasbeen emended to an aorist optative προτρέψαιτε (Burnet 1903).

i. ὑμεῖς ἄρα … τῶν νῦν ἀνθρώπων κάλλιστ´ ἂν προτρέψετε εἰς φιλοσοφίανyou then … the now men best an urge_on.2pl.fut.ind to philosophy

καὶ ἀρετῆς ἐπιμέλειαν;and virtue attention

‘Will you (pl.) then … be the best of men (alive) now to encourage (one) to philosophyand attention to virtue?’ (Plat. Euthyd. 275a)


(38) [[(9c)]]g,w = λ s ≤ w [ ( ∀ s′ : contribution of ἄν& equals are added to equals in s′ contribution of if-clause& (counterpart of) time (s′)⊆ topic time t Ri gives situations, not worlds& t does not precede now tense restricts Ri to non-past situations& ∃ s′′′ [ actual-world laws g(8) operate in s′′′ & s′′′ ≤ s′ ] SIM with laws L8& Cont(s′) ) ‘s′ is contextually appropriate’∃ s′′ [ s′ ≤ s′′ & the wholes are equal in s′′] ]Paraphrase: the conditional is true in a situation s ifff in a set of situations s′

– which overlap with (in the case of present tense) or follow (if future) (the counterpartof) the utterance time(tense restricts the modal base to non-past situations from different worlds)

– in which there is a counterpart of actual-world facts referred to by g(8),(similarity with res facts provides the ordering source)

– and in which (counterparts of) equals are added to equals,(if-clause)

– every situation s′ extends to the situation s′′, such that (counterpart of) the wholes areequal in s′′(then-clause)

(39)

The past general conditionals areminimally diffferent from the non-past exam-ples: theirmatrix clauses include a +excl feature in T, invoking past situations.These conditionals look like they don’t have ἄν—this is an illusion, created bythe fact that subjunctive + ἄν becomes optative without ἄν in the presence ofhigher past tense. The conditions that result in the optative mood in the sub-ordinate clause, thus, include (i), the presence of a quantifĳier (as opposed tonon-quantifĳicational contexts), (ii) quantifĳication over situations (rather thanwhole worlds), and (iii) a past main clause (the presence of the +excl featurein T).This brings us to another type of construction which involves the optative.

FLV conditionals and potential optative examples in general are the only type


of constructionwith ἄν that have a non-indicativemain clause.17 Because theseconstructions give rise to a counterfactual-like implicature, but are future-oriented, we propose that they include an accessibility relation which is bothrestricted by a +excl feature in C, like the counterfactual conditionals, and ele-mentswhich express future orientation (the actual nature of these elementsweleave for future research). Inmain clauses without pastmorphology, future ori-entation may be expressed by future tenses of the indicative, or by subjunctivemood. Sequence-of-moods in indirect discourse or in purpose clauses demon-strate that there is an alternation between indicative or future-oriented sub-junctive (in the presence of higher non-past) and optative mood (in the pres-ence of a higher past). Thus, the combination of future-oriented elements and+excl feature higher in the structure is expressed as an optative.The choice of mood morphology in Greek seems to form a scale from the

most specifĳic conditions triggering an optative (a higher +excl feature in addi-tion to the factors that otherwise trigger a subjunctive), to the ‘elsewhere’ caseof the indicative.Finally, consider the factors that influence the presence or absence of the

particle ἄν in conditionals. In the framework we adopt, all conditionals includea modal quantifĳier. In those conditionals where ἄν is absent, namely the par-ticular conditionals, there is a silent modal. The formal diffference we proposebetween them is that ἄν is a quantifĳier over situations—parts of possibleworlds,whereas the silentmodal quantifĳies overmaximal situations—wholeworlds. Inthe terms of Kratzer (1989), this roughly corresponds to the distinction betweengeneric universal quantifĳication (with ἄν) and accidental universal quantifĳica-tion (with the silent modal)—themismatch between Kratzer’s distinction andthe conditionals with andwithout ἄν concerns the counterfactual conditionals,in which the +excl feature restricts the (inherently situational) quantifĳicationto whole worlds.To summarize, we propose that the diffference between particular and all

other ‘textbook’ types of Greek conditionals lies in the nature of objects quanti-fĳied over—in the case of particular conditionals, whole worlds, and in the caseof other conditionals, situations. The semantic diffferences between the variouskinds of non-particular conditionals are due to the diffferent accessibility rela-tions that restrict the set of situations that ἄν quantifĳies over (the modal base).The diffferent relations arise from the diffferences between the contents of theC-T domains in these constructions, reflected in the overtmood and tensemor-phology in the main and subordinate verbs. Our main points about these aresummarized in the table below.

17) An anonymous reviewer points out that non-declarative main clauses such as hortatory sub-junctives, optatives of wish, and imperatives also occur in the main clause of conditionals.


(40) Table . Elements of modal constructions in Classical Greek.

quantifĳier/ accessibility tense situations conditional/its domain relation morphology per world construction

ἄν: worlds not fake single counterfactual,situations including w0 potential indicative

ἄν: worlds not n/a (future single FLV,situations including w0 situations) potential optative

ἄν: only includes s ≤ w0 true multiple iterativesituations time(s)⊆ topic time indicative

ἄν: may include s ≤ w0 true multiple general,situations time(s)⊆ topic time FMoreV©� : worlds contextually- true single particular,

determined FMostV

. Conclusions

We have presented a formal semantic treatment of the particle ἄν in ClassicalGreek, proposing that it denotes auniversal quantifĳier over situations—parts ofpossible worlds. Our proposal has accounted for several descriptive generaliza-tions regarding the use of the particle. Specifĳically, we have explained the cor-relation between the ‘fake’ past tensemorphology in sentences with ἄν and thepresenceof a counterfactual implicature in counterfactual conditionals and thepotential indicative construction.Utilizing the idea that past-tensemorphologyin such sentences reflects the presence of an exclusion feature in C, and notingthat future-oriented modal clauses acquire optative mood in the presence ofhigher past (due to sequence-of-moods), we have extended our account to thefuture less vivid conditionals and the potential optative construction.The semantic contrast with the iterative indicative construction, in which

the past is interpreted and no counterfactuality arises has been explained bythe placement of the exclusion feature in T, rather than C. As a result, theaccessibility relation yields a set of actual-world past situations, rather thannon-actual worlds for the modal to quantify over.We have also argued that the absence of the particle ἄν in the past general

conditionals is an illusion created by the sequence-of-moods phenomenon inwhich an optative without ἄν replaces a subjunctive verb accompanied by theparticle. The absenceof fakepast, and thepresenceof ἄν in general conditionalsresults in their non-counterfactual, multi-case interpretation.A suggestive generalization thatwe have not accounted for concerns the cor-

relation between the surface position of ἄν in the conditional and its interpre-tation: the particle’s surface position in counterfactual and FLV conditionals(which have the +excl feature in C) is in the consequent clause, but ἄν appears


on the surface in the antecedent clauses of general conditionals. We leave thissyntactic-semantic interface correlation as a challenge for future work.Our proposal has consequences for the formal semantic treatment of modal-

ity. A uniform treatment of the wide variety of constructions with ἄν requiresus to abandon an approach to similarity proposed in Arregui (2009). She pro-poses that a counterfactual sentence is a modal predicate of a specifĳic actual-world situation. Most-similar situations that are chosen for themodal to quan-tify over are those that contain a counterpart of the res situation. However,this notion of similarity will not work for the iterative uses, where the possi-bilities that the modal quantifĳies over include non-overlapping actual-worldsituations. Instead, we propose to treat conditionals (and other modal con-structions) as predicates of actual-world facts, conceptualized as features ofsituations. These facts can be modal themselves, representing the existence ofactual-world laws. Conditionals and other modal constructions are then pred-icated de re of these actual-world fact referents.18Space limitations have prevented us from being able to consider all the con-

structions inwhich ἄν appears inClassical Greek. Someof these, such as generictemporal clauses and free relativeswith ἄν have implications for the correct for-mal semantic treatment of similar constructions cross-linguistically.

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